Length-selective dielectrophoretic manipulation of single-walled carbon nanotubes

ABSTRACT

Systems &amp; methods for sorting single-walled carbon nanotubes (SWNTs) using an iDEP-based sorting device. The device includes an inlet channel with a constriction and the inlet channel splits into multiple different channels after the constriction—the multiple channels includes a center channel and at least one side channel. A sample is introduced into the iDEP sorting device containing a plurality of SWNTs of different lengths suspended in a fluid. An electrical field is applied to the sample between a first electrode in the center channel and a second electrodes at a proximal end of the inlet channel. The applied electrical field causes longer SWNTs to move towards the side channels while the shorter SWNTs move towards the center channel. Accordingly, a first plurality of shorter SWNTs is then collected from the center channel and a second plurality of longer SWNTs is collected from the at least one side channel.

RELATED APPLICATIONS

This application claims the priority benefit of U.S. Provisional PatentApplication No. 63/175,264, filed on Apr. 15, 2021 and entitled“LENGTH-SELECTIVE DIELECTROPHORETIC MANIPULATION OF SINGLE-WALLED CARBONNANOTUBES,” the entire contents of which are hereby incorporated byreference.

BACKGROUND

The present invention relates to systems and methods for sortingparticles and/or structures. In some implementations, the inventionrelates to systems and methods for sorting single-walled carbonnanotubes by length.

SUMMARY

Single-walled carbon nanotubes (SWNTs) possess unique physical, optical,and electrical properties with great potential for future nanoscaledevice applications. Common synthesis procedures yield SWNTs with largelength polydispersity and varying chirality. Electrical and opticalapplications of SWNTs often require specific lengths, but thepreparation of SWNTs with the desired length is still challenging.Insulator-based dielectrophoresis (iDEP) integrated into a microfluidicdevice has the potential to separate SWNTs by length. SemiconductingSWNTs of varying length suspended with sodium deoxycholate (NaDOC) showunique dielectrophoretic properties at low frequencies (<1 kHz) thatwere exploited here using an iDEP-based microfluidic constriction sorterdevice for length-based sorting. Specific migration directions in theconstriction sorter were induced for long SWNTs (>1000 nm) with negativedielectrophoretic properties compared to short (<300 nm) SWNTs withpositive dielectrophoretic properties. We report continuousfractionation conditions for length-based iDEP migration of SWNTs, andwe characterize the dynamics of migration of SWNTs in the microdeviceusing a finite element model. Based on the length and dielectrophoreticcharacteristics, sorting efficiencies for long and short SWNTs recoveredfrom separate channels of the constriction sorter amounted to >90% andwere in excellent agreement with a numerical model for the sortingprocess.

In some implementations, the systems and methods described hereinprovide a microfluidic device utilizing an insulator-baseddielectrophoretic (iDEP) technique for sorting single-walled nanotubes(SWNTs). The unit functions by producing inhomogeneous (non-uniform)electric field gradients that are utilized to move the SWNTs based onits dielectrophoretic (DEP) properties along with molecular lengths(long ≥1000 nm and short ≤300 nm versions) as a processing step. Theseimplementations provide a cost-effective and reliable method to separatethe SWNTs by size as a means to purify them through charge(attraction/repulsion) arrangement from their respective dipole moments.

In one embodiment, the invention provides an iDEP sorting device forsorting single-walled carbon nanotubes by length. The device includes aninlet channel with a constriction where the cross-sectional area of theinlet channel is reduced, a center channel, and at least one sidechannel. The inlet channel splits into multiple channels after theconstriction—the multiple channels include the center channel and the atleast one side channel. An electrode is positioned in the center channeland an electrical field source is configured to apply an electricalfield between the electrode and a proximal end of the inlet channel.

In another embodiment, the invention provides a method of sortingsingle-walled carbon nanotubes using an iDEP-based sorting device. TheiDEP-based sorting device includes an inlet channel with a constrictionwhere the cross-sectional area of the inlet channel is reduced at theconstriction and the inlet channel splits into multiple differentchannels after the constriction—the multiple channels includes a centerchannel and at least one side channel. A sample is introduced into theiDEP sorting device containing a plurality of single-walled carbonnanotubes of different lengths suspended in a fluid. An electrical fieldis applied to the sample between a first electrode in the center channeland a second electrode at a proximal end of the inlet channel. Theapplied electrical field causes longer SWNTs to move towards the sidechannels while the shorter SWNTs move towards the center channel.Accordingly, a first plurality of shorter SWNTs is then collected fromthe center channel and a second plurality of longer SWNTs is collectedfrom the at least one side channel.

Other aspects of the invention will become apparent by consideration ofthe detailed description and accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a schematic diagram of an iDEP-based sorter according to oneexample. The suspended SWNT sample is introduced via the inlet reservoirand channel. The sample flows through the channel toward a constrictionregion leading to five outlet branches which are labeled as S₁ and S₂for the two side outlets and C for the center outlet.

FIG. 1B is a diagram of the iDEP-based sorter of FIG. 1A showing theposition of small SWNT particles (e.g., 300 nm in length) exhibitingpositive DEP (pDEP) migrating toward the center outlet after migratingthrough the constriction.

FIG. 1C is a diagram of the iDEP-based sorter of FIG. 1A showing theposition of larger SWNT particles (e.g., 1000 nm in length) exhibitingnegative DEP (nDEP) migrating preferentially toward the side outlets.

FIG. 2A is a fluorescence image showing short SWNTs in the iDEP-basedsorter of FIG. 1A (at 1 kHz and 350 V) concentrating in the regions ofhighest electric field strength located in the center outlet channelindicative of pDEP.

FIG. 2B is a graph of normalized fluorescence intensity in the image ofFIG. 2A for all outlet channels demonstrating a higher analyteconcentration in the center outlet.

FIG. 2C is an AFM image of fractionated NaDOC-wrapped SWNTs collectedfrom the center outlet after sorting in the example of FIG. 2A.

FIG. 2D is a fluorescence image showing long SWNTs in the iDEP-basedsorter of FIG. 1A (at 1 kHz and 350 V) concentrating in the regions oflowest electric field strength in the side outlets indicative of nDEP.

FIG. 2E is a graph of normalized fluorescence intensity in the image ofFIG. 2D for all outlet channels demonstrating higher analyteconcentration in the side outlets.

FIG. 2F is an AFM image of fractionated NaDOC-wrapped SWNTs collectedfrom the side outlet in the example of FIG. 2D.

FIG. 3 is a graph of fluorescence intensity of SWNTs in two differentsamples (one with longer SWNTs and the other with short SWNTs) byanalyzing the intensity along the curved line in FIG. 2A and theGaussian fit for each peak, resulting in R=1.39.

FIG. 4 is a table of zeta potential and average lengths for SWNTs in thetwo different samples of FIG. 3.

DETAILED DESCRIPTION

Before any embodiments of the invention are explained in detail, it isto be understood that the invention is not limited in its application tothe details of construction and the arrangement of components set forthin the following description or illustrated in the following drawings.The invention is capable of other embodiments and of being practiced orof being carried out in various ways.

Applications of single-walled carbon nanotubes (SWNTs) in nanotechnologyrequire the understanding of their unique mechanical, electrical,optical, and structural properties. Metallic SWNTs are promising for thefield of nanoscale electronics, while semiconducting SWNTs can open thedoor for field-effect Schottky-type transistor applications, nanometersize devices, biological transporters, and biosensors. Due to their highphotostability and unique fluorescence emission in the IR range, whereautofluorescence in biological samples is minimal, SWNTs are alsoemployed as mechanical sensors in living cells. Their structural andchemical properties have also led to applications as atomic forcemicroscopy (AFM) probes.

An important factor for SWNT applications is the length of the SWNT. Forexample, in some implementations, there is a direct correlation of SWNTand multiwall carbon nanotube (MWNT) length with electrical and/orthermal conductivities. In addition, SWNT-based field-effect transistorshave the potential to replace silicon technologies. The length of SWNTshas a strong impact on the performance of such transistors. Also, themechanical, thermal, electrical, and electromagnetic properties ofMWNT-based epoxy resins depend on carbon nanotube length. SWNT length isimportant for reinforcing nanocomposites, because the length of the SWNTaffects both the Young's modulus and the load transfer between SWNTs andmatrix. Similarly, variations/improvement in the Young's modulus of SWNTcomposites is negligible when the length of the SWNT is less than 100 nmand only SWNTs with lengths greater than 1000 nm reinforce the polymermatrix significantly. Furthermore, in some implementations, CNTs may beused as an electrode material in Li-ion batteries and as catalystsupport in fuel cells. However, short CNTs (i.e., CNTs with a lengthless than 300 nm) provide better electrochemical performance duringcharging and discharging than longer CNTs. Also, the reversiblecapacities of long CNTs may be half of those of short CNTs. In addition,the charge-transfer resistance of long CNTs can be much higher thanthose of short carbon nanotubes. Furthermore, the toxicity offunctionalized MWNTs can be influenced by nanotube length. SWNTcytotoxicity studies revealed that the degree of functionalization isresponsible for the cytotoxic response of cells in a cell culture whichalso depends on the length of SWNTs. Therefore, length characterizationand control of CNTs (e.g., SWNTs) are useful in some nanotube-basedapplications and may be helpful in achieving “green chemistry”objectives.

Despite the importance of length in SWNT applications, many synthesismethods are unable to control or regulate length of the SWNT during thesynthesis process. In some implementations, the synthesis processesproduce mixtures of both metallic and semiconducting SWNTs with varyingchirality, a range of diameters (from ˜1 nm to ˜2 nm), and largevariations in length (e.g., from 10 nm up to >1 cm). The high-pressurecarbon monoxide (HiPCO) process, for example, is a common fabricationmethod yielding SWNT with diameters of ˜1 nm and lengths ranging fromseveral nanometers to several micrometers, containing more than 50chirality types. Accordingly, samples of SWNTs produced by the HiPCOprocess may show broadly varying electrical and optical properties,determined at least in part by the variations in chirality. In addition,SWNTs in samples may also form adducts and bundles held together by vander Waals forces, leading to a large variety of adduct species. Analternative synthesis strategy uses a focused ion beam, but thisapproach is expensive and has throughput limitations. Producing SWNTswith specific lengths or chirality at high yield is still challenging.The post-synthesis processing methods described in the examples hereinare, therefore, beneficial towards yielding pure SWNT fractions.

In some implementations, separation methods of SWNTs may take advantageof distinct electronic properties. For example, ultracentrifugationusing density gradient methods may be used to purify SWNTs and sort themby size. This method, however, is based on specific DNA oligomers usedto wrap the SWNTs, which limits large scale applications due to cost andoligomer availability. Furthermore, DNA-wrapped SWNTs have limitedstability in aqueous density gradients, which would require strippingthe DNA wrapping agent after separation. In other implementations, ionexchange and size-exclusion chromatography may be used as length sortingtools, and a combination of these two may be used for separation ofSWNTs by chirality with similar diameters. These separation techniquesalso require wrapping SWNTs with DNA with similar problems withstability, cost, and unwrapping. In other implementations,electrophoresis using DC electric fields might be used as a separationtool for SWNTs based on their diameter. However, this would be more adiagnostic than a production method because recovery from gels iscumbersome. Importantly, all these methods do not offer separation ofSWNTs in a continuous manner. Thus, a versatile fractionation orseparation approach for SWNTs by length is still lacking.

In other implementations, dielectrophoresis (DEP) may be used fornanoparticle separation. For example, DEP may be used to captureproteins, nucleic acids, as well as other biomolecules, and also carbonnanotubes. DEP may also be employed to sort SWNTs according to theirdielectric properties. When a cylindrical SWNT is introduced into anonuniform electric field, it will experience a force due to the induceddipole moment. The DEP force acting on a cylindrically shaped SWNT canbe expressed as

$\begin{matrix}{{\overset{\rightarrow}{F}}_{DEP} = {\frac{\pi r^{2}l}{3}\varepsilon_{m}{{Re}({CM})}{\nabla\left( \overset{\rightarrow}{E} \right)^{2}}}} & (1)\end{matrix}$

where r refers to the SWNT radius, l to its length, E to the electricfield, and ε_(m) to the permittivity of the suspending medium. Re(CM)denotes the frequency-dependent Clausius Mossotti factor. Depending onthe sign of Re(CM), SWNTs can be attracted to or repelled from regionsof high electric field strength. SWNTs experiencing positive DEP (pDEP)migrate toward the higher electric field, whereas SWNTs experiencingnegative DEP (nDEP) migrate toward the lower electric field.

In some implementations, insulator-based DEP (iDEP) may be utilized toproduce inhomogeneous electric field gradients. In an iDEP-basedmicrofluidic system, when an electrical potential is applied across thechannel, inhomogeneous electric field gradients are produced by theinsulating geometries or constrictions introduced in the channel. iDEPoffers several advantages such as simple fabrication and low cost usingwell established soft lithography techniques, avoiding electrodereactions within the devices. The electric field gradient can begenerated along the entire depth of the device. iDEP may be used toexamine DC and low-frequency DEP behavior of particles.

Studying single SWNT properties requires suspending them in solvents,and in many cases, aqueous media are preferred. However, due to strongvan der Waals interactions, SWNTs often aggregate in aqueous solutions.Thus, in some implementations, SWNTs are suspended using surfactants orbiomolecular wrapping agents. In some implementations, SWNTs may besuccessfully suspended with anionic surfactants such as sodiumdeoxycholate (NaDOC) or sodium dodecyl sulfate (SDS), and cationicsurfactants such as cetyltrimethylammonium bromide (CTAB), ssDNA, amongothers. The suspension of SWNTs with different surfactants orbiomolecules will eventually influence their surface charge and zetapotential (ζ). At low frequencies (<1 kHz), the DEP behavior ofNaDOC-suspended SWNTs mainly depends on the conductivity of the particleand the surrounding medium which, in turn, is determined by the zetapotential induced by surfactant wrapping. In this low-frequency regime,Re(CM) reduces to an expression for the particle and mediumconductivity, σ_(p) and am respectively, such thatRe(CM)=−1+σ_(p)/σ_(m). In the examples described herein, we exploit thisunique DEP behavior at low frequencies to induce size-selective iDEPmigration of SWNTs and exploit it for fractionation of SWNTs by length.

Chemicals. In the examples described below, sodium deoxycholate (NaDOC)for the suspension of SWNTs,N-(2-hydroxyethyl)piperazine-N′-2-ethanesulfonic acid (HEPES), andPluronic F-108 were purchased from Sigma-Aldrich (St. Louis, Mo.), andsodium hydroxide (NaOH) was purchased from Merck KGaA (Darmstadt,Germany). The SYLGARD 184 silicone elastomer kit forpolydimethylsiloxane (PDMS) for microdevice fabrication was obtainedfrom Dow Corning Corporation (Midland, Mich.). Glass slides (48 mm×60mm) for device assembly were purchased from Electron Microscopy Sciences(Hatfield, Pa.). Deionized (DI) water was produced with an Arium 611ultrapure water system from Sartorius (Gottingen, Germany). For atomicforce microscopy imaging, Muscovite Mica (V-1, sheet size 25×25 mm,thickness 0.15-0.21 mm) was purchased from Ted Pella, Inc. (Redding,Calif.), and (3-aminopropyl)triethoxysilane (APTES) was obtained fromSigma-Aldrich (Hamburg, Germany). A Malvern Zetasizer Nano ZS instrument(Westborough, Mass.) was used for surface charge measurements. Mediumconductivity was measured by a Thermo Scientific Orion 3-starconductivity meter (Waltham, Mass.).

Microdevice Fabrication. Microfluidic constriction sorter devices werefabricated with soft lithography techniques. The microfluidic chiplayout and channel structures were designed using AutoCAD software(Autodesk, San Rafael, Calif.) which was used to construct a chromephotomask (Photo Sciences, Inc., Torrance, Calif.). The pattern wastransferred to a 4-in. silicon master wafer using SU-8 negativephotoresist (Microchem, Westborough, Mass.). Then the PDMS elastomerbase was mixed with curing agent at a 10:1 ratio (w/w), poured over themaster wafer, and degassed for 30 min, and the PDMS cast was cured in anoven for 4 h at 80° C. The cast was subsequently peeled off the masterwafer, and reservoirs were punched manually with a punch, with a 1.5 mmdiameter at the inlets and 3 mm diameter at the outlets for fluidicaccess. The PDMS cast was cut into appropriate pieces, and these slabsand microscope glass slides were cleaned with 2-propanol and distilledwater in an ultrasonic bath for 2 min, dried with nitrogen, and baked ona hot plate for 30 s at 90° C. The PDMS slab and glass slides were thentreated with oxygen plasma in a plasma cleaner oven (PDC-001: HarrickPlasma cleaner/sterilizer, Ithaca, N.Y.) at high RF (18 W) for 30 s.Both surfaces were then brought into contact, and the device wasirreversibly bonded with the glass slide to create fluid channels. Thechannels were washed several times with distilled water, and then thesurface was treated with Pluronic F-108 (1% w/v) and incubatedovernight, as previously described. The assembled PDMS microfluidic chiphad an overall length of 5 mm with a 30 μm wide constriction region; theinlet channel was 100 μm wide, and all outlets were 20 μm wide as shownin FIG. 1. All channels were ≈20 μm high.

SWNT Sample Preparation. SWNTs used for the experiments were suspendedwith the surfactant NaDOC. NaDOC was dissolved at a concentration of 1%(w/v) in 10 mM HEPES buffer (pH 7.2) containing 1% (w/v) F108. About 1mg of SWNTs was carefully transferred into a clean glass scintillationvial with a spatula, and 1 mL NaDOC solution was added. To wrap andsolubilize SWNTs, they were sonicated at 20 kHz at 10 W using a 2 mmmicrotip sonicator (Sonics & Material INC, Danbury, Conn.). Two types ofNaDOC-coated samples were prepared with different sonication times. Toobtain short SWNTs (sample A), the solution was sonicated for 60 min.After sonication, the sample was centrifuged for 10 min at 14,800 rpm.After centrifugation, the supernatant was collected for the experiments.This sample was diluted at a ratio of 10:1 with HEPES buffer containingF108. To obtain long SWNTs (sample B), the solution was sonicated for 10s. After sonication, the SWNT suspension was transferred to an Eppendorftube and centrifuged (Sigma 1-14 centrifuge, Germany) at 2000 rpm for 10min. All samples were stored at 4° C. prior to the experiments.

Detection and Data Analysis. SWNT fluorescence was excited with a 561 nmsolid-state laser (500 mW cw, Cobolt Jive, Cobolt) coupled through aneutral density filter (NDC-50C-4M, Thorlabs) which was used to adjustthe intensity of the laser. The laser beam was directed into a high-NAobjective (CFI plan-Apo IR, 60×, Nikon, Japan), and the same objectivewas used to collect the fluorescence light through a dichroic beamsplitter (630 DCXR; AHF Analysentechnik). After the beam splitter, thefluorescence light was further filtered through a 900 nm long-passfilter (F47-900; AHF, Analysentechnik). SWNTs were imaged with an InGaAsinfrared camera (XEVSSHS-1.7-320 TE-1, Xenics, Leuven, Belgium). Imageswere captured at a 100 ms frame time, and data analysis was performedwith Micromanager software (ImageJ, version 1.52a, NIH, Bethesda, Md.).

SWNT Sorting and Size Characterization. To characterize lengthdistributions of SWNTs in samples A and B and in the fractionatedsamples, dynamic light scattering (DLS) was carried out with a ZetasizerNano ZS instrument (Malvern Panalytical, Westborough, Mass.). During thesorting experiments, flow rates were maintained at 25 μL/h with asyringe pump (HA1100, Instech, Plymouth Meeting, Pa.), while a potentialof 350 V was applied at a frequency of 1000 Hz. After ˜3 h of sorting atoptimized potential and frequency, —20 μL SWNT sample was accumulatedfrom the center outlet and then diluted to 1 mL with sample buffer forDLS. In addition, atomic force microscopy (AFM) was used to image SWNTs.Briefly, mica (Grade V1, 25 mm×25 mm, Ted Pella, Redding, Calif.) wastreated with APTES, and a drop of the respective SWNT sample wasincubated on the mica surface for 5 min. After incubation, the micasurface was cleaned with DI water and dried for the AFM measurements. ACypher S AFM (Asylum Research, Goleta, Calif.) was used for SWNT imagingusing tapping mode in air with a Si tip with a spring constant of 42 N/mand a resonance frequency of 300 kHz (AC160 TS C2, Olympus, Dusseldorf,Germany). About 35-40 nanotubes were measured for each sample todetermine the average length.

Further, samples A and B were mixed and a similar fractionationexperiment performed as described above. The mixed SWNT sample wasprepared by adding 500 μL each of sample A and sample B in an Eppendorftube. The mixed sample was introduced into the microdevice through theinlet reservoir with a flow rate of 25 μL/h and subjected tofractionation at 1000 Hz and with an applied potential of 350 V. Todetermine the separation resolution R, we quantified the fluorescenceintensity along a curved line spanning the start of the outlet channels(see, e.g., line 201 in FIG. 2A) with Image G (version 1.52a), fit thedata with a Gaussian in Origin software (OriginPro 2017, version 94E)and calculated R according to R=1.18×(x_(A)−x_(B))/(w_(A)+w_(B)), wherex_(A) and x_(B) refer to the locations of the peak maxima, and w_(A) andw_(B) correspond to the full width at half-maximum, respectively.

We studied the migration of SWNTs wrapped with sodium deoxycholate(NaDOC) in a continuous-flow iDEP microfluidic constriction sorter. FIG.1A depicts the microfluidic sorter consisting of an inlet channel 101, aconstriction 103, and five outlet channels. The five outlet channelsinclude a center outlet channel C, a first S1 outlet channel 105 on afirst side of a flow axis of the inlet channel 101, a second S1 outletchannel 107 on a second side of the flow axis of the inlet channel 101,a first S2 outlet channel 109 on the first side of the flow axis of theinlet channel 101, and a second S2 outlet channel 111 on the second sideof the flow axis of the inlet channel 101. As illustrated in greaterdetail in FIGS. 1B and 1C, the five outlet channels diverge from theinlet channel 101 after the constriction 103 of the inlet channel. Inthis example, the center outlet channel C extends along the same flowaxis as the inlet channel 101. The first and second S1 outlet channels105, 107 divert from the inlet channel 101 on opposite sides of the flowaxis of the inlet channel 101 at a first distance from the start of theconstriction 103. The first and second S2 outlet channels 109, 111divert from the inlet channel 101 on opposite sides of the flow axis ofthe inlet channel 101 at a second distance from the start of theconstriction 103. The second distance is longer than the first such thatthe first and second S2 outlet channels 109, 111 each divert from theinlet channel 101 after the first and second S1 outlet channels 105, 107(along the flow path) between the center outlet channel C and arespective S1 outlet channel 105, 107.

As also illustrated in the examples of FIGS. 1B and 1C, each outletchannel C, 105, 107, 109, 111 includes a small diameter section 113 anda large diameter section 115. The small diameter section 113 for eachoutlet channel is positioned between the constriction 103 of the inletchannel 101 and the large diameter section 115 of the outlet channel.The small diameter sections 113 provides an extension and, in somecases, a variation of the constriction 103 in order to influence theiDEP electric field gradient of the device.

The device includes an inlet opening 121 at a proximal end of the inletchannel 101 (i.e., the end of the inlet channel 101 opposite theconstriction 103). The device also includes a plurality of outletopenings 123 positioned at a distal end of each outlet channel C, 105,107, 109, 111. The inlet opening 121 is coupled (or selectivelycoupleable) to an inlet reservoir (not picture) holding the fluid sampleto be pumped through the device. Each outlet opening is coupled (orselectively coupleable) to a different outlet reservoir (not pictured)configured to receive the fluid sample after it has moved through thedevice. In some implementations, each outlet opening of the device iscoupled to a different outlet reservoir (e.g., five outlet reservoirs inthe example of FIGS. 1A through 1C). However, in other implementations,the outlet opening 123 for similarly positioned outlet channels onopposite sides of the flow axis of the inlet channel 101 may be coupledto the same outlet reservoir (e.g., the outlet openings 123 of the firstand second S1 outlet channels 105, 107 are both coupled to a firstoutlet reservoir, the outlet openings 123 of the first and second S1outlet channels 109, 111 are both coupled to a second outlet reservoir,and the outlet opening 123 of the center outlet channel C is coupled toa third outlet reservoir. In still other implementations, the outletopenings 123 for all of the outlet channels may be coupled to a singleshared outlet reservoir.

A first electrode 125 is positioned in the inlet channel 101 (e.g., nearthe inlet opening 121 as illustrated in the example of FIG. 1A) and asecond electrode 127 is positioned in the center outlet channel C (e.g.,near the outlet opening 123 of the center outlet channel C asillustrated in the example of FIG. 1A). In some implementations, anelectrical field is applied to the device by coupling the firstelectrode 125 to ground, coupling the second electrode 127 to an ACvoltage source, and operating the AC voltage source to apply theelectrical field between the first electrode 125 and the secondelectrode 127.

The unique geometry of the constriction 103 creates localized electricfield nonuniformities near the constriction 103 and the outlet channelsvia the electrical potential applied between the inlet and outletreservoirs (i.e., between the first electrode 125 and the secondelectrode 127). The electric field maximum is located in the centeroutlet channel and the minimum in the side outlet channels. Due to thenonuniform electric field, the resulting DEP forces deflect particlesbased on their length and surfactant wrapping properties into differentoutlets. As illustrated in the example of FIG. 1B, relatively smallerSWNTs (e.g., with lengths of approximately 500 nm) exhibit positive DEP(pDEP) and migrate towards the electrical field maximum in the centeroutlet channel C. Conversely, as illustrated in the example of FIG. 1C,relatively larger SWNTs (e.g., with lengths of approximately 1000 nm)exhibit negative DEP (nDEP) and migrate towards the electrical fieldminimum in the first and second S1 outlet channels 105, 107.

Bulk fluid transport of a SWNT suspension through the sorter device isinduced by external pressure (e.g., a mechanical pump or a syringe pumpconfigured to pump fluid from the inlet reservoir into the inlet opening121 of the device). In some implementations, the device illustrated inthe example of FIGS. 1A through 1C is operated by constant pumping of afluid including the SWNTS suspension into the inlet opening 121 whichthe fluid drains through the outlet openings 123 into one or more outletreservoirs and the applied electric field gradient causes SWNTs to besorted in the outlet flow into each respective outlet reservoir (e.g.,such that SWNTs collect in different outlet reservoirs based on length).In other implementations, the fluid sample a volume of the fluid sampleis introduced into the inlet opening 121 and prevented from draining outof the device through the outlet openings 123 (e.g., byplugging/blocking the outlet openings 123 or by positioning of theoutlet openings 123 above the fluid line). After the fluid is placedwithin the device (without any flow in or out of the device), theelectric field is applied and the SWNTs move towards the various outletchannels depending on their length. The length-sorted SWNTs may then beremoved from the device through the outlet openings 123 (e.g., byremoving the plug and allowing the fluid to drain from the device, or byusing a device such as a syringe to remove the sample fluid from eachseparate outlet channel).

SWNT Sample Characterization. SWNT suspensions prepared with longsonication times (>60 min) contained short SWNTs with high zetapotential, exhibiting pDEP (Re(CM)>0). In contrast, short sonicationtimes resulted in SWNTs with lower zeta potential but increased lengthsdisplaying nDEP (Re(CM)>0). In some experiments, two samples wereprepared accordingly using different sonication times, primarilycontaining short (sample A) and long (sample B) SWNTs. The lengthdistributions of samples A and B, as well as the zeta potentials, wereinvestigated with dynamic light scattering (DLS) and atomic forcemicroscopy (AFM) imaging as summarized in the table of FIG. 4. AFM andDLS measurements showed the average SWNT length in sample A to be366.9±16.8 and 324.5±16.6 nm, respectively. For sample B, the averagelength was determined as 1145.7±435.0 nm with AFM and 932.3±34.0 nm withDLS.

Prediction of iDEP Separation of SWNTs. Based on the size distributionsin the two samples and varying zeta potentials, the expected migrationbehavior of SWNTs is nontrivial. We therefore first conducted anumerical study to predict the SWNT migration in the constriction sorterdevice of FIGS. 1A through 1C. SWNT lengths from 50 to 2000 nm werestudied with the numerical model, spanning the size range exploredexperimentally in samples A and B. FIG. 1B shows a snapshot imageobtained from the numerical simulation after passage through theconstriction 103 for the shorter SWNTs (i.e., —300 nm long) with pDEPproperties (Re(CM)=13.44). From the inlet, 100 particles were released,and a majority of them was found in the center channel C. FIG. 1C showsthe migration of the longer SWNTs (i.e., —1000 nm long) with nDEPproperties (Re(CM)=—1.18). In the case of the sample containing thelonger SWNTs (i.e., Sample B as illustrated in FIG. 1C), SWNTs weresorted with a preference into the side outlets where the electric fieldstrength is lowest, which is expected for nanotubes with nDEP(Re(CM)<0). This example demonstrates that short SWNTs with pDEPproperties can be sorted from large SWNTs with nDEP into differentoutlets.

FIG. 1B (higher particle count in the center channel) and FIG. 1C(higher particle count in side channel) show distinct migrationpreference into different outlets for the two selected SWNT speciesexhibiting variations in length and DEP properties. To quantify thepreference of migration, the recovery efficiency of the S1 outletchannels 105, 107, % E_(S1), was calculated based on particle countsfound in each outlet channel:

$\begin{matrix}{{\% E_{S1}} = \frac{N_{S1}}{N_{S1} + N_{S2} + N_{C}}} & (2)\end{matrix}$

where N_(S1), N_(S2), and N_(C) are the number of particles found in thetwo S1 outlet channels 105, 107, the two S2 outlet channels 109, 111,and the center outlet channel C. Similarly, the efficiencies of the S2outlet channels 109, 111 (% E_(S2)) and the center outlet channel (%E_(C)) were obtained. For the two cases shown in FIGS. 1B and 1C, therecovery efficiency was 83.9% in the case of 1000 nm SWNTs with nDEP forthe sum of S1 and S2 outlets, and 83.1% for the 300 nm SWNTs exhibitingpDEP in the center outlet.

The numerical model allows to investigate % E for monodisperse SWNTs. Tocarefully map the migration behavior over a broad range of lengthdistribution of surfactant wrapped SWNTs originating from the suspensionand wrapping process, we studied % E of various SWNT lengths rangingfrom 50 nm up to 2000 nm with the numerical model. We studied both nDEPand pDEP properties for each SWNT length to account for well-wrapped(pDEP and high ζ) as well as such SWNT species exhibiting nDEP resultingfrom uncomplete wrapping and low ζ. The numerical study revealed thatthe sorting efficiencies in the center outlet increased for decreasingthe length of SWNTs in the case of pDEP. For long SWNTs with nDEPproperties, this trend is significantly different. The longer the SWNTspecies, the stronger their preferred migration to the side outlets(with preference for the S2 side outlets).

Experimental Observation of iDEP Separation of SWNTs. Based on thisanalysis, a recovery efficiency ˜90.2% can theoretically be achieved forSWNTs of 50 nm length with pDEP causing preferred migration into thecenter outlet. SWNTs of the same size with nDEP properties, however, didnot show a preferential sorting efficiency. In contrast, for a 2000 nmlong SWNT with nDEP properties, a % E of ˜92.9% can be achieved due topreferred migration into the four side channels combined. A generaltrend was observed in which longer SWNTs with nDEP properties (resultantfrom lower preferentially migrate into the side channels and can besorted from larger SWNTs with pDEP properties (resultant from higherNote that experimentally, we expect improved wrapping properties, higherzeta potentials, and therefore pDEP for the shorter SWNTs, becauseshorter SWNTs result from longer sonication and suspension times, asfurther detailed below. The converse holds for longer SWNTs.

To test this length-dependent migration behavior experimentally, amicrofluidic constriction sorter was employed using a sample with amajority of short SWNTs (sample A) and one with longer SWNTs (sample B).SWNTs were introduced into the microdevice through the inlet opening 121with a syringe pump at a flow rate of 25 μL/h. In this case, SWNTs weredistributed evenly in the microchannel. Next, DEP-based migration wasinduced by varying the applied potentials at a flow rate of 25 μL/h. Nopreferred migration into any outlet channel was observed below 300 V.Fractionation behavior was investigated with a frequency of 1000 Hz andan applied potential of 350 V where DEP forces were sufficiently high.

To characterize the length distribution in samples A and B, AFM imagingand DLS were used before and after the DEP migration experiments. Wealso characterized for each sample before and after the sortingexperiment. At low frequencies, the sign of Re(CM) of semiconductingSWNTs is governed by the conductivity of the medium and the particle.While the particle conductivity is predominantly determined by thedouble layer contributions arising from the Stern layer and diffuselayer conductance, it is also dependent on the zeta potential of thecharged particle suspended in an electrolyte. Therefore, the zetapotential has an impact on the Clausius Mossotti factor and DEPproperties of SWNTs, as shown previously. For sample A (shorter SWNTs),the zeta potential was measured to be ˜49.7±1.3 mV prior to sorting,which is in agreement with the previous reports. For sample B (longerSWNTs), the zeta potential was measured as ˜19.8±1.7 mV (see also, thetable of FIG. 4).

Both samples were subjected to fractionation in the constriction sorter,while the sorting behavior was monitored with near-infrared fluorescencemicroscopy. FIG. 2A shows the fractionation behavior of sample A (i.e.,the shorter SWNTs) as observed during the sorting experiment,demonstrating that the majority of SWNTs migrated to the center channel,where the electric field strength was highest. This migration behaviorcorresponds to that predicted by the numerical model for the pDEP casefor SWNT lengths ≤300 nm as demonstrated in FIG. 1B. FIG. 2B representsthe normalized intensity in the different outlets, demonstrating thatmaximum intensity was observed in the center outlet and that the shortSWNTs migrated into the center outlet. FIG. 2C shows an AFM image ofNaDOC-wrapped SWNTs collected from the center outlet after 3 h offractionation. AFM imaging revealed an average length of 288.8±139.3 nm.Consistent with this result, the DLS measurement gave an average SWNTlength of 278.8±4.5 nm and of ˜51.3±0.7 mV for the center outletfraction. The average length after fractionation is thus slightlyreduced compared to sample A before fractionation, and the zetapotential is slightly increased. The side outlet fractions from the samefractionation experiment were combined and analyzed. Both AFM(581.0±253.0 nm) and DLS (506.2±26.3 nm) indicated a larger averagelength than the starting sample A, and the zeta potential of ˜23.6±4.5mV was considerably reduced. We attribute this outcome to the fact thatthe sorter was capable of fractionating the somewhat polydisperse sampleA. In addition we note, that this sorting behavior is in excellentagreement with the numerical results. The table of FIG. 4 lists averagelengths and values for the original and fractionated samples. We notethat length distributions of SWNTs analyzed by AFM and DLS are in goodagreement, although slightly higher average lengths are obtained withAFM measurements. We attribute this difference to the length weightinginherent to the DLS technique and to a systematic bias in the SWNTlength determination via AFM. The latter may result from undercountingof overlapped SWNTs and preferential deposition on the surface prior toAFM imaging. However, a significance test confirmed that the two methodsdo not differ (p=0.05).

Next, the fractionation behavior of sample B (long SWNTs) prepared withshorter sonication time was investigated. Long SWNTs suspended by 10 ssonication have a lower zeta potential and showed nDEP characteristicsin agreement with previous reports. In the sorting experiment, theypreferably migrated to the low electric field regions in the sideoutlets, shown in FIG. 2D. This observation was confirmed by thefluorescence intensity quantification, where the highest intensity wasfound in the side outlets as shown in FIG. 2E. In agreement with thepreferred migration of longer SWNTs with nDEP behavior into the sideoutlets, AFM analysis (as shown in FIG. 2F) resulted in an averagelength of 1462.2±412.8 nm. DLS characterization confirmed the preferredmigration of long SWNTs into the side outlets and showed an averagelength of 1245.3±239.1 nm and ζ of −10.7±1.2 mV. The much smallerfluorescence intensity observed in the center outlet channel isattributed to smaller SWNTs with pDEP behavior migrating to the centerchannel, which was also confirmed by the length analysis of the fractioncollected in the center outlet after sorting. Both DLS and AFMcharacterization revealed a shorter average length (see FIG. 4). Thisresult is again in agreement with the numerical model for SWNTs≥1000 nmand nDEP.

The dependence of the DEP response on can be explained by the variationsin surface conductance induced through the quality of the surfactantwrapping. While longer SWNTs exhibit smaller ζ, the shorter SWNTs,subjected to more rigorous sonication and longer wrapping times, showhigh ζ. The zeta potential influences the SWNT surface conduction,because it determines the magnitude of the diffuse layer conductance,λ_(s,d), as well as the Stern layer conductance, λ_(s,s), which both sumup to the surface conductance, λ_(s). The surface conductance can beused to describe the SWNT conductivity, via σ_(P)=2λ_(sa) ⁻¹, where a isthe radius, and intrinsic conductivity is neglected. A lower zetapotential then leads to lower λ_(s) and consequently lower σ_(p), sinceσ_(p) governs the dielectrophoretic response of SWNTs at a given σ_(m)via the Re(CM)=—1+σ_(p)/σ_(m).

To further characterize the resolution of the SWNT separation, weanalyzed the intensity of SWNTs from samples A and B at a location closeto the constriction 103, right before the start of the three types ofoutlet channels. For this purpose, we conducted a spatial intensityanalysis along the line 201 in FIG. 2A. The intensity distributionsalong this line 201 are shown in FIG. 3, which allow for the calculationof R between sample A and B. In the graph of FIG. 3, line 301 indicatesthe fluorescence intensity from Sample A (smaller SWNTs), line 303indicates the fluorescence intensity from Sample B (longer SWNTs), andline 305 indicates the Gaussian fit for each curve. From this analysis,the spatial separation resolution along this line resulted in 1.39.

Finally, we conducted a fractionation experiment of the entire sizerange, by combining samples A and B. The AFM analysis revealed anaverage length of 1372.3±251.6 nm in the side outlets and an averagelength of 366.2±221.2 nm in the center outlet. This is in very goodagreement with the migration experiments carried out for the individualsamples A and B, as demonstrated in the table of FIG. 4, and confirmedthe working principle of the SWNT fractionation approach based on DEP atlow frequency.

In summary, we conducted a study of SWNT fractionation based on thelength and DEP properties using an insulator-based dielectrophoresisconstriction sorter. We present a numerical model that predicts recoveryefficiencies up to ˜90% in selected outlets of a constriction sorterbased on SWNT length and DEP properties. Experimentally, two samplesdiffering in lengths and DEP properties showed migration behaviormatching the numerical model. Long SWNTs with small zeta potentialsexhibited nDEP and migrated preferably into the side outlets of thesorter. In contrast, small SWNTs with high negative zeta potentials werefractionated into the center channel. We demonstrate that the variationsin zeta potential caused by surfactant wrapping and sonication time canbe conveniently exploited to fractionate SWNTs by DEP. The resultantresolution for the two length distributions assessed experimentally wasalmost at baseline resolution demonstrating a good separation quality.The employed constriction sorter is capable of sorting SWNTs incontinuous mode which is advantageous for technological applications inwhich larger quantities of SWNTs are required. Future optimization ofthe geometry of the device as well as the electrical driving parameterscould further improve the length selectivity of this fractionationapproach.

Certain systems methods and examples relating to the subject matterabove was published in an article authored by the inventors entitled“Length-Selective Dielectrophoretic Manipulation of Single-Walled CarbonNanotubes,” Rabbani et al., Anal. Chem. 2020, 92, 8901-8908, the entirecontents of which are incorporated herein by reference.

Accordingly, the systems and methods described above provide, amongother things, length-selective dielectrophoretic manipulation ofsingle-walled carbon nanotubes. Other features and advantages are setforth in the following claims.

What is claimed is:
 1. An iDEP device for sorting single-walled carbon nanotubes by length, the iDEP device comprising: an inlet channel including a constriction, wherein a cross-sectional area of the inlet channel reduces at the constriction; a center channel; at least one side channel, wherein the inlet channel splits into multiple channels after the constriction, the multiple channels including the center channel and the at least one side channel; an electrode positioned in the center channel; and an electrical field source configured to apply an electrical field between the electrode and a proximal end of the inlet channel.
 2. The iDEP device of claim 1, wherein the center channel is aligned with a flow axis of the inlet channel, wherein the at least one side channel includes a first plurality of side channels on a first side of the flow axis of the inlet channel and a second plurality of side channels on a second side of the flow axis of the inlet channel.
 3. The iDEP device of claim 1, wherein the inlet channel diverges from the constriction into the center channel and the at least one side channel.
 4. The iDEP device of claim 3, wherein a width of the inlet channel before the constriction is greater than a width of the constriction of the inlet channel, wherein a width of the center channel is less than the width of the constriction of the inlet channel, wherein a width of the at least one side channel is less than the width of the constriction of the inlet channel, and wherein channels of the iDEP device are formed of an insulating material such that variations in the widths of the channels produces an electric field gradient when the electric field is applied between the electrode and the proximal end of the inlet channel.
 5. The iDEP device of claim 4, wherein the width of the inlet channel before the constriction is 100 μm, wherein the width of the constriction of the inlet channel is 30 μm, wherein the width of the center channel is 20 μm, and wherein the width of the at least one side channel is 20 μm.
 6. A method of sorting single-walled carbon nanotubes by length using the iDEP device of claim 1, the method comprising: introducing a fluid suspension of single-walled carbon nanotubes into the iDEP device at the proximal end of the inlet channel; and operating the electrical field source to apply the electrical field between the electrode and the proximal end of the inlet channel, wherein applying the electrical field to the fluid suspension causes a first plurality of single-walled carbon nanotubes to migrate towards the center channel and causes a second plurality of single-walled carbon nanotubes to migrate towards the at least one side channel, wherein an average length of the first plurality of single-walled carbon nanotubes is less than an average length of the second plurality of single-walled carbon nanotubes.
 7. The method of claim 6, wherein introducing the fluid suspension into the iDEP device at the proximal end of the inlet channel includes pumping the fluid suspension into the iDEP device at the proximal end of the inlet channel at a flow rate of 25 μL/h.
 8. The method of claim 6, wherein operating the electrical field source to apply the electrical field includes operating the electrical field source to apply an alternating current (AC) electrical field with a magnitude of at least 350 V between the electrode and a second electrode positioned at the proximal end of the inlet channel.
 9. The method of claim 8, wherein operating the electrical field source to apply the electrical field further includes operating the electrical field source to apply the AC electrical field with a frequency of 1000 Hz.
 10. The method of claim 6, further comprising preparing the fluid suspension of single-walled carbon nanotubes by: combining a sample of single-walled carbon nanotubes with a surfactant solution containing a surfactant diluted in a buffer fluid, and sonicating the fluid suspension for a predetermined period of time, wherein the predetermined period of time is selected based at least in part on a desired length of single-walled carbon nanotubes to be isolated from the sample of single-walled carbon nanotubes.
 11. The method of claim 6, wherein the surfactant solution includes a sodium deoxycholate (NaDOC) surfactant diluted to a concentration of 1% in an N-(2-hydroxyethyl)piperazine-N′-2-ethanesulfonic acid (HEPES) buffer fluid.
 12. The method of claim 6, wherein sonicating the fluid suspension includes sonicating the fluid suspension at 20 kHz at 10 W.
 13. The method of claim 6, wherein the predetermined period of time of sonication is increased in order to isolate shorter single-walled carbon nanotubes with a length below a first threshold length by increasing the positive DEP response of the shorter single-walled carbon nanotubes, and wherein the predetermined period of time of sonication is increased in order to isolate longer single-walled carbon nanotubes with a length above a second threshold length by increasing the negative DEP response of the longer single-walled carbon nanotubes.
 14. The method of claim 13, further comprising: removing the isolated shorter single-walled carbon nanotubes from the center channel; and removing the isolated longer single-walled carbon nanotubes from the at least one side channel.
 15. A method of sorting single-walled carbon nanotubes, the method comprising: introducing a sample into an iDEP sorting device, the sample containing a plurality of single-walled carbon nanotubes of different lengths suspended in a fluid, the iDEP sorting device including an inlet channel including a constriction, wherein a cross-sectional area of the inlet channel reduces at the constriction; a center channel, and at least one side channel, wherein the inlet channel splits into the center channel and the at least one side channel after the constriction; applying an electrical field to the sample, wherein the electrical field is applied between a first electrode in the center channel and a second electrode at a proximal end of the inlet channel; collecting a first plurality of single-walled carbon nanotubes from the center channel; and collecting a second plurality of single-walled carbon nanotubes from the at least one side channel, wherein the single-walled carbon nanotubes of the first plurality have a length that is shorter than the single-walled carbon nanotubes of the second plurality. 